What was found
CLIMBING THROUGH FL 320 TO FL 350 WITH ALL CONDITION NORMAL, ACFT SHUDDERED AND SWERVED SLIGHTLY, THEN BEGAN CONTINUOUS THUMPS, BOTH AUDIBLE AND CLEARLY FELT THROUGH AIRFRAME. THERE WERE NO ECAM ADVISORIES, BUT NR 1 ENGINE N1 DECREASED TO APPROX 60 PERCENT. BROUGHT NR 1 THROTTLE TO IDLE AND THUMPS STOPPED. STILL NO OBVIOUS INSTRUMENT INDICATIONS AND NO VIBRATION INDICATION ON ECAM ENGINE PAGE. ADVANCED THROTTLE SLIGHTLY AND GOT IMMEDIATE RETURN OF VIBRATIONS. SHUT DOWN ENGINE, DECLARED EMERGENCY, AND DIVERTED. R&R NR 1 ENGINE IAW WORK CARD 44T0701-1, OPS CHECK NORMAL IAW WORK CARD 44T0701-1.